arXiv subjects

Michael Kastner

Publications and source records attributed to Michael Kastner.

At least 37 records · Page 2Linked to original sources

arXiv2018

Subexponentially growing Hilbert space and nonconcentrating distributions in a constrained spin model

Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an "order parameter" may be present.

cond-mat.stat-mech↗

arXiv2018

Universal equilibrium scaling functions at short times after a quench

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

cond-mat.stat-mech↗

arXiv2017

Noninvasive Measurement of Dynamic Correlation Functions

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-$1/2$ models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

quant-ph↗

arXiv2017

Quantum effects in the cooperative scattering of light by atomic clouds

Scattering of classical light by atomic clouds induces photon-mediated effective long-range interactions between the atoms and leads to cooperative effects even at low atomic densities. We introduce a novel simulation technique that allows us to investigate the quantum regime of the dynamics of large clouds of atoms. We show that the fluorescence spectrum of the cloud can be used to probe genuine quantum cooperative effects. Signatures of these effects are the occurrence, and the scaling behavior, of additional sidebands at twice the frequency of the classical Mollow sidebands, as well as an asymmetry of the Mollow triplet.

physics.optics↗

arXiv2017

$N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems

Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on long-range quantum spin models that illustrate this scaling behaviour, and provide indications for its common occurrence by making use of Lieb-Robinson bounds. I argue that these findings may help in understanding the extraordinarily short equilibration timescales predicted by typicality techniques.

cond-mat.stat-mech↗

arXiv2016

Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($\propto 1/r^α$ with distance $r$), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of $α$ for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on $α$ as well as on the quench parameters.

cond-mat.quant-gas↗

arXiv2015

Entanglement-enhanced spreading of correlations

Starting from a product initial state, equal-time correlations in nonrelativistic quantum lattice models propagate within a lightcone-like causal region. The presence of entanglement in the initial state can modify this behavior, enhancing and accelerating the growth of correlations. In this paper we give a quantitative description, in the form of Lieb-Robinson-type bounds on equal-time correlation functions, of the interplay of dynamics vs. initial entanglement in quantum lattice models out of equilibrium. We test the bounds against model calculations, and also discuss applications to quantum quenches, quantum channels, and Kondo physics.

quant-ph↗

arXiv2015

Simulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories

A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Going to higher orders of the BBGKY hierarchy allows for a systematic refinement of the method. Quantum correlations are treated through both, the Wigner function sampling and the BBGKY evolution, bringing about highly accurate estimates of correlation functions. The method is particularly suitable for long-range interacting systems, and we demonstrate its power by comparing with exact results as well as other numerical methods. As an application we compute spin squeezing in a two-dimensional lattice with power-law interactions and a transverse field, which should be accessible in future ion trap experiments.

cond-mat.stat-mech↗

arXiv2015

Relaxation timescales and prethermalisation in d-dimensional long-range quantum spin models

We report analytic results for the correlation functions of long-range quantum Ising models in arbitrary dimension. In particular, we focus on the long-time evolution and the relevant timescales on which correlations relax to their equilibrium values. By deriving upper bounds on the correlation functions in the large-system limit, we prove that a wide separation of timescales, accompanied by a pronounced prethermalisation plateau, occurs for sufficiently long-ranged interactions.

cond-mat.stat-mech↗

arXiv2015

Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions

We study the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like $r^{-α}$ with the distance $r$. Our focus is on exponents $α$ between 0 and 6, where the interplay of long- and short-range features gives rise to a complex phenomenology and interesting physical effects, and which is also the relevant range for experimental realizations with cold atoms, ions, or molecules. We present analytical and numerical results, providing a comprehensive picture of spatio-temporal propagation. Lieb-Robinson-type bounds are extended to strongly long-range interactions where $α$ is smaller than the lattice dimension, and we report particularly sharp bounds that are capable of reproducing regimes with soundcone as well as supersonic dynamics. Complementary lower bounds prove that faster-than-soundcone propagation occurs for $α<2$ in any spatial dimension, although cone-like features are shown to also occur in that regime. Our results provide guidance for optimizing experimental efforts to harness long-range interactions in a variety of quantum information and signaling tasks.

quant-ph↗

arXiv2014

Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points

The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we can only sample a small fraction. We investigate the interplay between this restricted sample size and the physical features of the potential energy landscape for the two-dimensional $XY$ model in the absence of disorder with up to $N=100$ spins. Using an eigenvector-following technique, we numerically compute stationary points with a given Hessian index $I$ for all possible values of $I$. We investigate the number of stationary points, their energy and index distributions, and other related quantities, with particular focus on the scaling with $N$. The results are used to test a number of conjectures and approximate analytic results for the general properties of energy landscapes.

cond-mat.stat-mech↗

arXiv2014

Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field

The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying the concavity properties of entropies. The microcanonical entropy s(e,m) is obtained as a function of the energy e and the magnetization vector m in the thermodynamic limit. Since, for this model, e is uniquely determined by m, the same information can be encoded either in s(m) or s(e,m1,m2). Although these two entropies correspond to the same physical setting of fixed e and m, their concavity properties differ. The entropy s_h(u), describing the model at fixed total energy u and in a homogeneous external magnetic field h of arbitrary direction, is obtained by reduction from the nonconcave entropy s(e,m1,m2). In doing so, concavity, and therefore equivalence of ensembles, is restored. s_h(u) has nonanalyticities on surfaces of co-dimension 1 in the (u,h)-space. Projecting these surfaces into lower-dimensional phase diagrams, we observe that the resulting phase transition lines are situated in the positive-temperature region for some parameter values, and in the negative-temperature region for others. In the canonical setting of a system coupled to a heat bath of positive temperatures, the nonanalyticities in the microcanonical negative-temperature region cannot be observed, and this leads to a situation of effective nonequivalence even when formal equivalence holds.

cond-mat.stat-mech↗

arXiv2014

Quantum correlations and entanglement in far-from-equilibrium spin systems

By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments, and can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: we characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a non-perturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed.

cond-mat.quant-gas↗

arXiv2014

Spreading of Perturbations in Long-Range Interacting Classical Lattice Models

Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the dependence of the system's dynamics on a perturbation of the initial state. The effect of the perturbation is found to be effectively restricted to the interior of a causal region of logarithmic shape, with only small, algebraically decaying effects in the exterior. A refined bound, sharper than conventional Lieb-Robinson bounds, is required to correctly capture the shape of the causal region, as confirmed by numerical results for classical long-range $XY$ chains. We discuss the relevance of our findings for the relaxation to equilibrium of long-range interacting lattice models.

cond-mat.stat-mech↗

arXiv2013

Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking of a recently developed ion-trap based quantum simulator.

quant-ph↗

arXiv2013

Universal threshold for the dynamical behavior of lattice systems with long-range interactions

Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^α with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction range α, we find evidence for the existence of a threshold at α=d/2, dependent on the spatial dimension d, at which the relaxation behavior changes qualitatively and the corresponding scaling exponents switch to a different regime. Based on analytical as well as numerical observations in systems of vastly differing nature, ranging from quantum to classical, from ferromagnetic to antiferromagnetic, and including a variety of lattice structures, we conjecture this threshold and some of its characteristic properties to be universal.

cond-mat.stat-mech↗

arXiv2013

Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model

We study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method. On the basis of these stationary points, we analyze the complexity and other quantities related to the glass transition of the model and compare these finite-system quantities to their exact counterparts in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2012

Exploring the energy landscape of XY models

We investigate the energy landscape of two- and three-dimensional XY models with nearest-neighbor interactions by analytically constructing several classes of stationary points of the Hamiltonian. These classes are analyzed, in particular with respect to possible signatures of the thermodynamic phase transitions of the models. We find that, even after explicitly breaking the global O(2) symmetry of the XY spins, an exponentially large class of stationary points are singular and occur in continuous one-parameter families. This property may complicate the use of theoretical tools developed for the investigation of phase transitions based on stationary points of the energy landscape, and we discuss strategies to avoid these difficulties.

cond-mat.stat-mech↗